I was watching the cartoon on PBS "Arthur" and Arthur doesn't listen to his father and uses baking soda instead of baking powder and his "cake" fails. But at the end of the cartoon, Arthur's dad says "But look Arthur, you may haven't made a cake but you made great brownies."

Is that the only difference between say a chocolate cake and chocolate brownies?

I was watching the cartoon on PBS "Arthur" and Arthur doesn't listen to his father and uses baking soda instead of baking powder and his "cake" fails. But at the end of the cartoon, Arthur's dad says "But look Arthur, you may haven't made a cake but you made great brownies."

Is that the only difference between say a chocolate cake and chocolate brownies?

Brownies are flatter, denser, and moister than cake. If a cake failed to rise, and it would if you used baking soda instead of powder, I suppose you could call it brownies instead. They would not be as good as purpose-made brownies, though.